Hello, it’s been a while. Allow me to get back in great style by showing this quite satisfactory game of chess that I played. Start with the best by test. e4 d5 exd5 Qxd5 Nf3 Qd8 Nc3 b6 d4 Bb7 Be3 e6 Bb5+ c6 Ba4 h6 O-O Nf6 Already here things start to get weird, […]

## Integer Ordered Triplets

Distinguishing cases, find the number of ordered triplets (x, y, z) of positive integers such that Let be the number of such triplets for n. We can get a first recursive formula by noticing that if and then . From this we deduce that as one can easily check that the cases where at least […]

## Seemingly Difficult, But Not Really

There are 12 red balls, 15 white balls and 17 black balls in a box. A person extracts all the balls, one at a time. What’s the probability that all the red balls will be extracted before the white balls and that all the white balls will be extracted before the black balls? There are […]

## Attack the King Side? Close the center!

This week I’ve reached 2000 ELO rapid and 1900 ELO blitz on lichess, and I started playing many games I enjoyed more than usual. This was one of them. 1. Nf3 c5 2. d4 cxd4 3. Nxd4 Nc6 4. Nc3 Nf6 5. b3 e6 6. Bb2 Bb4 7. a3 Ba5 8. e3 O-O Already, a […]

## Python Collage and Contour

This set of Python programs is about creating a collage and then adding a contour to it. import numpy as np import matplotlib.pyplot as plt import matplotlib.image as im import random random.seed(123) l = [] a = list(range(1, 37)) random.shuffle(a) for i in a: if i == 35: continue image = im.imread(‘images/collagephoto{}.jpg’.format(i)) l.append(image) l1 = […]

## Got A Match?

Another incredible Chick Corea piece is ‘Got a match?’, which he first played with the ‘Elektrik Band’. It was released in 1986, and it’s a very particular kind of shred, where Chick and his band ‘show off’ their technique. Its live versions are very nice, and the characteristics of these exhibitions are: they are usually […]

## Inequality From Today’s Contest

Today a math contest I organized was held and I think this was the most difficult exercise overall. There are m distinct positive even integers and n distinct positive odd integers that add up to 1987. Find the maximum of 3m + 4n. So we have this sum of integers We can write that Now […]

## Quarantine And Bijections

Now the majority of Italy is in lockdown again. So, why not spend some time doing combinatorics. Today’s subject is bashing sums without having to do any calculation. Let’s say we have this sum: One way to do it would be differentiating , then multiplying the result by x and differentiating again. Then we get […]

## On the razor’s edge

This game was really strange. There have been various moments where I could have really taken the upper hand, but I missed many of them. So, I consider it instructive to show how a game could be improved. I played black, and as I usually do when e5 is played, I responded with c5, going […]

## Natural Language Processing with Dante

In this period, I’m studying natural language processing and its applications. One of my favourite tricks is generating text which reminds someone’s style. For example, here I will show an AI (trained for 100 minutes and just two epochs) that has learned to fake Dante’s Divine Comedy. import tensorflow as tffrom tensorflow import kerasimport numpy […]